Fixed Point Results for Fuzzy Enriched Contraction in Fuzzy Banach Spaces with Applications to Fractals and Dynamic Market Equillibrium
We introduce fuzzy enriched contraction, which extends the classical notion of fuzzy Banach contraction and encompasses specific fuzzy non-expansive mappings. Our investigation establishes both the presence and uniqueness of fixed points considering this broad category of operators using a Krasnosel...
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MDPI AG
2024-10-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/8/10/609 |
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| author | Muhammad Shaheryar Fahim Ud Din Aftab Hussain Hamed Alsulami |
| author_facet | Muhammad Shaheryar Fahim Ud Din Aftab Hussain Hamed Alsulami |
| author_sort | Muhammad Shaheryar |
| collection | DOAJ |
| description | We introduce fuzzy enriched contraction, which extends the classical notion of fuzzy Banach contraction and encompasses specific fuzzy non-expansive mappings. Our investigation establishes both the presence and uniqueness of fixed points considering this broad category of operators using a Krasnoselskij iterative scheme for their approximation. We also show the graphical representation of fuzzy enriched contraction and analyze its graph for different values of beta. The implications of these findings extend to significant results within fuzzy fixed-point theory, enriching the understanding of iterative processes in fuzzy metric spaces. To demonstrate the versatility of our innovative concepts and the associated fixed-point theorems, we provide illustrative examples that showcase their applicability across diverse domains, including the generation of fractals. This demonstrates the relevance of fuzzy enriched contraction to iterated function systems, enabling the study of fractal structures under various contractive conditions. Additionally, we explore practical applications of fuzzy enriched contraction in dynamic market equilibrium, offering new insights into stability and convergence in economic models. Through this unified framework, we open new avenues for both theoretical advancements and real world applications in fuzzy systems. |
| format | Article |
| id | doaj-art-a311ff0637c44ece8bf66055c12b7419 |
| institution | OA Journals |
| issn | 2504-3110 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-a311ff0637c44ece8bf66055c12b74192025-08-20T02:11:09ZengMDPI AGFractal and Fractional2504-31102024-10-0181060910.3390/fractalfract8100609Fixed Point Results for Fuzzy Enriched Contraction in Fuzzy Banach Spaces with Applications to Fractals and Dynamic Market EquillibriumMuhammad Shaheryar0Fahim Ud Din1Aftab Hussain2Hamed Alsulami3Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, PakistanAbdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, PakistanDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaWe introduce fuzzy enriched contraction, which extends the classical notion of fuzzy Banach contraction and encompasses specific fuzzy non-expansive mappings. Our investigation establishes both the presence and uniqueness of fixed points considering this broad category of operators using a Krasnoselskij iterative scheme for their approximation. We also show the graphical representation of fuzzy enriched contraction and analyze its graph for different values of beta. The implications of these findings extend to significant results within fuzzy fixed-point theory, enriching the understanding of iterative processes in fuzzy metric spaces. To demonstrate the versatility of our innovative concepts and the associated fixed-point theorems, we provide illustrative examples that showcase their applicability across diverse domains, including the generation of fractals. This demonstrates the relevance of fuzzy enriched contraction to iterated function systems, enabling the study of fractal structures under various contractive conditions. Additionally, we explore practical applications of fuzzy enriched contraction in dynamic market equilibrium, offering new insights into stability and convergence in economic models. Through this unified framework, we open new avenues for both theoretical advancements and real world applications in fuzzy systems.https://www.mdpi.com/2504-3110/8/10/609Hutchinson–Barnsley operatorsfuzzy enriched contractionfuzzy enriched iterated function systemattractorfractalsdynamic market equilibrium |
| spellingShingle | Muhammad Shaheryar Fahim Ud Din Aftab Hussain Hamed Alsulami Fixed Point Results for Fuzzy Enriched Contraction in Fuzzy Banach Spaces with Applications to Fractals and Dynamic Market Equillibrium Fractal and Fractional Hutchinson–Barnsley operators fuzzy enriched contraction fuzzy enriched iterated function system attractor fractals dynamic market equilibrium |
| title | Fixed Point Results for Fuzzy Enriched Contraction in Fuzzy Banach Spaces with Applications to Fractals and Dynamic Market Equillibrium |
| title_full | Fixed Point Results for Fuzzy Enriched Contraction in Fuzzy Banach Spaces with Applications to Fractals and Dynamic Market Equillibrium |
| title_fullStr | Fixed Point Results for Fuzzy Enriched Contraction in Fuzzy Banach Spaces with Applications to Fractals and Dynamic Market Equillibrium |
| title_full_unstemmed | Fixed Point Results for Fuzzy Enriched Contraction in Fuzzy Banach Spaces with Applications to Fractals and Dynamic Market Equillibrium |
| title_short | Fixed Point Results for Fuzzy Enriched Contraction in Fuzzy Banach Spaces with Applications to Fractals and Dynamic Market Equillibrium |
| title_sort | fixed point results for fuzzy enriched contraction in fuzzy banach spaces with applications to fractals and dynamic market equillibrium |
| topic | Hutchinson–Barnsley operators fuzzy enriched contraction fuzzy enriched iterated function system attractor fractals dynamic market equilibrium |
| url | https://www.mdpi.com/2504-3110/8/10/609 |
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